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Segment Analysis - Schedule of Segment Reporting (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jun. 30, 2025
Jun. 30, 2024
Jun. 30, 2025
Jun. 30, 2024
Sep. 30, 2024
Segment Reporting Information [Line Items]          
Total revenues $ 34,828.8 $ 27,069.7 $ 99,654.8 $ 68,748.8  
Operating revenues: 1,024.3 913.7 2,924.6 2,516.1  
Net operating revenues (loss): 488.3 468.5 1,467.7 1,312.4  
Net contribution: 378.4 377.3 1,146.4 1,043.1  
Segment income 236.9 243.7 737.9 664.5  
Net operating loss within Corporate (10.9) (26.9) (40.6) (55.3)  
Overhead costs and expenses (140.4) (128.8) (397.7) (353.2)  
Income before tax 85.6 88.0 299.6 256.0  
Assets 34,265.6   34,265.6   $ 27,466.3
Corporate          
Segment Reporting Information [Line Items]          
Total revenues 15.7 8.3 43.5 31.9  
Operating revenues: 15.7 8.3 43.5 31.9  
Net operating revenues (loss): (10.9) (26.9) (40.6) (55.3)  
Assets 1,055.2   1,055.2   1,123.5
Eliminations          
Segment Reporting Information [Line Items]          
Total revenues (10.7) (13.0) (45.8) (36.6)  
Operating revenues: (10.7) (13.0) (45.8) (36.6)  
Commercial          
Segment Reporting Information [Line Items]          
Net contribution: 124.3 168.7 409.9 414.4  
Segment income 80.2 125.7 279.1 298.5  
Commercial | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 34,028.8 26,410.3 97,389.8 66,867.4  
Operating revenues: 225.8 262.2 706.7 661.1  
Net operating revenues (loss): 168.3 220.5 550.8 548.1  
Assets 5,403.9   5,403.9   5,387.0
Institutional          
Segment Reporting Information [Line Items]          
Net contribution: 136.4 104.8 382.7 307.5  
Segment income 87.4 62.2 252.0 188.7  
Institutional | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 626.0 508.9 1,726.8 1,408.0  
Operating revenues: 626.0 508.9 1,726.8 1,408.0  
Net operating revenues (loss): 200.1 157.7 565.1 456.1  
Assets 26,168.2   26,168.2   19,492.9
Self-Directed/Retail          
Segment Reporting Information [Line Items]          
Net contribution: 76.4 63.7 227.4 196.2  
Segment income 41.2 27.6 120.1 89.5  
Self-Directed/Retail | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 115.7 104.1 378.8 317.1  
Operating revenues: 114.2 96.2 331.7 290.7  
Net operating revenues (loss): 80.6 68.5 239.2 209.8  
Assets 1,141.0   1,141.0   1,024.1
Payments          
Segment Reporting Information [Line Items]          
Net contribution: 41.3 40.1 126.4 125.0  
Segment income 28.1 28.2 86.7 87.8  
Payments | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 53.3 51.1 161.7 161.0  
Operating revenues: 53.3 51.1 161.7 161.0  
Net operating revenues (loss): 50.2 $ 48.7 153.2 $ 153.7  
Assets $ 497.3   $ 497.3   $ 438.8